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A proof of the trace theorem of Sobolev spaces
on Lipschitz domains


Author: Zhonghai Ding
Journal: Proc. Amer. Math. Soc. 124 (1996), 591-600
MSC (1991): Primary 46E35
DOI: https://doi.org/10.1090/S0002-9939-96-03132-2
MathSciNet review: 1301021
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Abstract: A complete proof of the trace theorem of Sobolev spaces on Lipschitz domains has not appeared in the literature yet. The purpose of this paper is to give a complete proof of the trace theorem of Sobolev spaces on Lipschitz domains by taking advantage of the intrinsic norm on $H^{s}(\partial\Omega)$. It is proved that the trace operator is a linear bounded operator from $H^{s}(\Omega)$ to $H^{s-\frac{1}{2}}(\partial\Omega)$ for $\frac{1}{2}<s<\frac{3}{2}$.


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Additional Information

Zhonghai Ding
Affiliation: Department of Mathematics Texas A&M University College Station, Texas 77843
Address at time of publication: Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, Nevada 89154
Email: dingz@nevada.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03132-2
Keywords: Sobolev spaces, Lipschitz domains, trace theorem
Received by editor(s): September 15, 1994
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society